Squaring both sides of an equation is irreversible. Is Cubing both sides of an equation reversible? Provide numerical examples to help support your answer.

Answers

Answer 1

Answer:

Cubing both sides of an equation is reversible.

Step-by-step explanation:

Squaring both sides of an equation is irreversible, because the square power of negative number gives a positive result, but you can't have a negative base with a positive number, given that the square root of a negative number doesn't exist for real numbers.

In case of cubic powers, this action is reversible, because the cubic root of a negative number is also a negative number. For example

[tex]\sqrt[3]{x} =-1[/tex]

We cube both sides

[tex](\sqrt[3]{x} )^{3} =(-1)^{3} \\x=-1[/tex]

If we want to reverse the equation to the beginning, we can do it, using a cubic root on each side

[tex]\sqrt[3]{x}=\sqrt[3]{-1} \\\sqrt[3]{x}=-1[/tex]

There you have it, cubing both sides of an equation is reversible.


Related Questions

Zech deposited $5,600 in an account, which compounded 1.9 percent quarterly, and left it there for 10 years. What was the amount in the account at the end of 10 years? Round to the nearest dollar.

Answers

Answer:

$6769

Step-by-step explanation:

To calculate the amount, we make use of the compound interest formula

A = P(1+r/n)^nt

where A is the amount which we are to calculate

P is the amount deposited which is $5,600

r is the rate which is 1.9% or 1.9/100 = 0.019

t is the number of years = 10

n is the number of times the interest is compounded per year which is 4(quarterly means every 3 months and there are 4 quarters in a year)

Plugging all these values, we have

A = 5,600(1+ 0.019/4)^40

A = 5,600( 1 + 0.00475)^40

A = 5,600(1.00475)^40

A = $6768.75

Which is $6769 to the nearest dollars

Help me please I think you have to find the area

Answers

Answer:

I got B) ; 54m2

Step-by-step explanation:

the above diagram is a trapezium.

the area is gotten by; 1/2 (a+b)h

a = shortest side.

b = the longer side that is directly opposite to (a).

h = height.

1/2(3 + 9)9

1/2 by 12 by 9

to get 54

Factor the quadratic equation below to reveal the solutions. X^2+4x-21=-9

Answers

Answer:

-6 and 2

Step-by-step explanation:

Bob has taken out a loan of $15,000 for a term of 48 months (4 years) at an interest rate of 6.5%. Using the amortization table provided, what will be his total finance charge over the course of his loan?

Monthly Payment per $1,000 of Principal
Rate 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $30.65 $23.71 $19.57
7.0% $86.53 $44.77 $30.88 $23.95 $19.80
7.5% $86.76 $45.00 $31.11 $24.18 $20.04
8.0% $86.99 $45.23 $31.34 $24.41 $20.28
8.5% $87.22 $45.46 $24.65 $24.65 $20.52
9.0% $87.45 $45.68 $31.80 $24.89 $20.76
A.
$355.65
B.
$975.00
C.
$1,682.40
D.
$2,071.20
E.
$17,071.20

Answers

The total finance charge over the course of his loan is $2071.20.

It is required to find the total finance charge.

What is simple & compound interest?

Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time. Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. Formula. S.I. = (P × T × R) ⁄ 100.

Given that:

Loan= $15,000

The table tells you that Bob's monthly payment on a 4-year loan at 6.5% will be 23.71 per thousand borrowed.

The sum of those 48 payments is ...

=48 × $23.71 =

 =$1138.08

That means, Bob pays $138.08 in total finance charge for each $1000 he borrows. He is borrowing 15 times $1000.

so his total finance charge will be

= 15 × $138.08

= $2071.20

Therefore, the total finance charge over the course of his loan is $2071.20.

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Answer:

D.

$2,071.20

Step-by-step explanation:

Find the equation of the line shown.
HELP PLEASEEE

Answers

Answer:

y = x+6

Step-by-step explanation:

The y intercept is 6  ( where it crosses the y axis)

We need to find the slope

For each y unit it goes up, it goes to the right 1 x unit

m = 1/1 = 1

We can use the slope intercept form of the equation

y = mx+b  where m is the slope and b is the y intercept

y = 1x+6

y = x+6

five whole numbers are written in order (4, 6, x, y, 10). The mean and median of the five numbers are the same. Work out the values of x and y.

Answers

Answer:

x = 7

y = 8

Step-by-step explanation:

Knowing that the mean is equal to the median, we can formulate the following equation:

⅕(4 + 6 + x + y + 10) = x

Simplifying it, we get:

y = 4x - 20

Now, we know that both x and y are between 6 and 10 and that y is greater than x;

Mathematically, we have the conditions:

6 =< x =< 10

6 =< y =< 10

y > x

If we apply the second condition, i.e. the restrictions on the y-values, we find that x has to be between 6.5 and 7.5, i.e. 6.5 =< x =< 7.5;

This means x has to 7 since it can only be a whole number and this is the only whole number between 6.5 and 7.5;

Once we know this, we can find y simply by subbing it into the equation formulated previously:

y = 4(7) - 20

y = 8

Cesar and Jocelyn are planning their trips to three countries next year. There are 7 countries they would like to visit. One trip will be one week long, another two days, and the other two weeks.

Answers

Answer:

They need five weeks to make all their travels.

Step-by-step explanation:

Given that Cesar and Jocelyn are planning their trips to three countries next year.

One trip will be one week long, another two days, and the other two weeks.

In conclusion, they need five weeks to make this travel.

What is the solution to the equation 3(2x + 5) = 3x + 4x?
a
X= 15
b.
X= 5
X=0
dx = 4

Answers

Answer: A

Step-by-step explanation:

Distribute the 3(2x+5) which gives you 6x+15. Than add 3x+4x which gives you 7x. Subtract the 6x giving you 15=x or 15=1x, divide the one to get the x alone and you get A.

What is the value of the expression below ? 2[32-(4-1)]

There is a 3 in between the ) 3 ] but it looks like square / cubes something

Answers

The value of the expression [tex]2[32-(4-1)][/tex] is [tex]58[/tex] by simplifying.

Simplification

Simplification is the process of replacing a mathematical expression with an equivalent one, that is simpler and usually shorter.

How to simplify an algebraic expression?

Apply the BODMAS rule to simplify the algebraic expression.

Given that the expression is [tex]2[32-(4-1)][/tex]

First, simplify the bracket [tex](4-1)[/tex]

Then, [tex]2[32-(4-1)]=2[32-3][/tex]

Simplify the bracket [tex][32-3][/tex]

Then, [tex]2[32-3]=2[/tex] × [tex]29[/tex]

Multiply the numbers [tex]2[/tex] and [tex]29[/tex]

[tex]2[/tex] × [tex]29=58[/tex]

Hence, the expression [tex]2[32-(4-1)][/tex] is simplified to [tex]58[/tex].

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The radius of a circle is 5 m. Find its area in terms of .

Answers

Answer:

78.5 m²

Step-by-step explanation:

Area formula: πr²

Plug it in: (3.14)(5m)²

Answer: 78.5 m²

Picture attachment below

Answers

Answer:

$4.50 for 9 cans

Step-by-step explanation:

What was the percentage decrease in the number of accidents between 1950 and 1976?

Answers

Answer:

the percentage decrease in the number of accidents between 1950 and 1976 is (25.9)

A circle has a diameter that measures
8 inches. What is the area of the circle to the nearest tenth? Use 3.14 for pi.

Answers

Answer:

50.24inches

Step-by-step explanation:

Your diameter is 8 inches so divide that by two to get a radius of 4 multiply 4 by itself and multiply that (16) by pi.(it gives you 50.24)

An emergency plumber charges $65 as a call-out fee plus an additional $75 per hour. He arrives at a house at 9:30 am and works to repair a water tank. If the total repair bill is $195.25 at what time was the repair completed?

Answers

Answer:

Around 11:15 am

Step-by-step explanation:

Let h represents the number of hours the plumber works

Since the plumber charges $65 fee plus $75 per hour, the bill can be calculated by:

→ bill = 65 + 75h

Since the bill is $195.25

→ 195.25 = 65 + 75h

→ 75h = 130.25

→ h = 1.74

1.74 implies that the plumber worked almost 1 hour and 45 minutes. Since the plumber started at 9:30, the repair was completed around 11:15 am.

How do you solve this question? With a step by step explanation please!

Answers

[tex]\frac{1}{4}x + 2 = -3 + \frac{1}{2} x[/tex]

First, we will take [tex]\frac{1}{4}[/tex]x to the right hand side of the equation, and -3 to the left hand side. In doing so, their signs will change (that is, they will be subtracted from the side that they are moved to).

2 -(-3) = [tex]\frac{1}{2} x - \frac{1}{4} x[/tex]

2 + 3 = [tex]\frac{1}{4}[/tex]x

[tex]\frac{1}{4} x = 5[/tex]

Now, we will multiply both sides by 4, so as to find x.

[tex]\frac{1}{4} x[/tex] x 4 = 5 x 4

x = 20

Therefore, x = 20.

you are mountain climbing with a friend. you need to reach a ledge that is 22 feet above you

Answers

Answer:

x+22

Step-by-step explanation:

you don't know what elevation you are on and you need to go up 22 feet more to the ledge above you.


The figure below is an isosceles triangle. What is the perimeter of the triangle in terms of a
and c?

Answers

Hey there! I'm happy to help!

-------------------------------------------------------------------

WHAT IS THE PERIMETER?

The perimeter is just the distance around a shape. If you put a fence around a field, the length of all of the fencing is the perimeter.

-------------------------------------------------------------------

WHAT IS AN ISOSCELES TRIANGLE?

An isosceles triangle is a triangle that has at least two sides that have the same length! In our triangle, we have two sides that have the value of a, so that makes it isosceles!

-------------------------------------------------------------------

THE SOLUTION

In our problem, we want to find the perimeter of this triangle in terms of a and c. When we say in terms of, it just means that our answer will include a and c instead of finding a number value.

The perimeter is the sum of each of these sides. This means that the perimeter is a+a+c, which is also 2a+c.

Therefore, the perimeter of this isosceles triangle is 2a+c.

-------------------------------------------------------------------

I hope that this helps! Have a wonderful day! :D

The slope of a line is 2. The y-intercept of the line is -6 Which statements accurately describe how to graph the function?
Locate the ordered pair (0-6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line.
Draw a line through the two points.
Locate the ordered pair (0-6). From that point on the graph, move up 2left 1 to locate the next ordered pair on the line
Draw a line through the two points.
Locate the ordered pair (-60). From that point on the graph, move up 2, right 2 to locate the next ordered pair on the line.
Draw a line through the nivo points.
Locate the ordered pair (-60). From that point on the graph, move up 2. left 1 to locate the next ordered pair on the line.
Draw a line through the two points,
Mark this and retum
Save and Exit
Subemt

Answers

Answer: A

Step-by-step explanation:

We know the y intercept is -6 so the first point will be  (0,-6)   and we also know that the slope is  2/1  so after plotting (0.-6) you will have to go up by two and  1 unit to the right.  

Answer:

The answer is A!

Step-by-step explanation:

I just did it and it is right! Have an absolutaly amazing day! :) :) :) :)

type an equation for the line shown in the graph

Answers

0x+2 =y
So technically x+2=y

Hi so i am writing a movie but i need ideas

Answers

A coming of age story about two childhood best friends who grow apart
You can write about many interesting things. For example, you can write about your life or make up characters.

I hope this helps you!!!!

.- Alicia tiene una finca de 1 km2 de superficie. Dedica 28 hm2 a cultivar trigo, 3.900 dam2 a plantar olivos y el resto lo ha plantado de girasoles.¿ Cuántos metros cuadrados ocupan los girasoles?

Answers

Answer:

330 000 m²

Step-by-step explanation:

1. Area of farm

[tex]A = \text{1 km}^{2} \times\left (\dfrac{\text{1000 m}}{\text{1 km}} \right )^{2}= \text{1 000 000 m}^{2}[/tex]

2. Area for wheat

[tex]A = \text{28 hm}^{2} \times \left (\dfrac{\text{100 m}}{\text{1 hm}}\right)^{2} = \text{280 000 m}^{2}[/tex]

3.Area for olive trees

[tex]A = {\text{3900 dam}^{2} \times \left (\dfrac{\text{10 m}}{\text{1 dam}}\right )^{2}}= \text{390 000 m}^{2}[/tex]

4. Area for sunflowers

Total area                  =                          1 000 000 m²

- Area for wheat        = 280 000 m²

- Area for olive trees = 390 000                                  

                                                                 670 000      

Area for sunflowers =                              330 000 m²

Sunflowers occupy 330 000 m².

Which function has the same range as f(x)=-2√x-3+8?

Answers

Answer:

[tex]g(x)=-\sqrt{x+3}+8[/tex]

Step-by-step explanation:

got it right

g(x) = - √x + 3 +8 has the same range.

What is the range of a function simple?

The variety of a feature is described as a set of solutions to the equation for a given input. In different words, the range is the output or y fee of a characteristic. There is the most effective range for a given function.

What is range in a relation?

The set which contains all the first elements of all the ordered pairs of relation R is known as the domain of the relation.

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A sphere has a radius of 5 inches. What is its volume?
Sphere V=
WIT
4
72
3
1. Substitute the radius into the formula:
V=4(5)
V = (125)
2. Evaluate the power,
3. Simplify:
V=
it in, 3

Answers

Answer:

500/3

Step-by-step explanation:

just did it on edg!

What is the equation of 4over 3 equal Y

Answers

Answer:

3y = 4 or 3y - 4 =0

Step-by-step explanation:

[tex] \frac{4}{3} = y \\ 4 = 3y \\ 3y - 4 = 0 \\ [/tex]

Zachary and Heather are measuring the growth of a plant for a science experiment. They stopped recording the growth after week 6. Which of the following could be a reasonable estimate for the value of the plant height at week 10?

35 inches


47 inches


50 inches


43 inches

will mark brainliest

Answers

Answer:

43, it raises by 4 each time. good luck!

Step-by-step explanation:

3) Factor x2 – 8x – 9.
Check

Answers

Answer:

(x-9)(x+1)

Step-by-step explanation:

factor using the box method or quadratic formula.

Answer:

(x - 9)(x + 1)

Step-by-step explanation:

Given

x² - 8x - 9

Consider the factors of the constant term (- 9) which sum to give the coefficient of the x- term (- 8)

The factors are - 9 and + 1, since

- 9 × 1 = - 9 and - 9 + 1 = - 8, thus

x² - 8x - 9 = (x - 9)(x + 1)

Which is a solution to (x − 2)(x + 10) = 13?

Answers

Answer:

3

Step-by-step explanation:

3-2=1

3+10=13

1x13=13

Carlos keeps track of his math scores of tests. His scores on his math tests are
the following: 100, 88, 50, 50, 90, 70, 80 What is the:
Median?
Mode?
Mean?
Range?

Answers

Answer:

Median: 75

Mode: 50

Mean: ≈ 75.4

Range: 50

Step-by-step explanation:

Median:

Arrange the numbers in order:

50, 50, 70, 80, 88, 90, 100

There is no exact middle number.

[tex]70 + 80 = 150\\150/2 = 75[/tex]

The median is about 75.

Mode:

50, 50, 70, 80, 88, 90, 100

"50" appears the most.

The mode is 50.

Mean:

Add all numbers in the set.

[tex]100+88+50+50+90+70+80 = 528[/tex]

Divide by the number of values in the set.

[tex]528/7 = 75.4285714286[/tex]

75.4285714286 ≈ 75.4

The mean is about 75.4.

Range:

Subtract the smallest number in the data set from the largest number in the data set.

[tex]100-50=50[/tex]

The range is 50.

Brainilest appreciated.

About how many times greater is the volume of the cylinder than the volume of the cone?

Answers

Your answer is 3 times larger.

The volume of any cone is 1/3 the volume of the cylinder that could be formed around that cone, therefore the volume of any cylinder is 3 times larger than the volume of the cone that could fit inside.

We know this is true because the equation for the volume of a cone is (1/3) πr²h, and the equation for the volume of a cylinder is πr²h

I hope this helps!

In this equation what is the

Answers

Answer:

multiplication i think? correct me if im wrong:)

Step-by-step explanation:

bye.

The answer is [ C. Multiply ]

The inverse operation of division is multiplication and vice versa.

The inverse operation of subtraction is addition and vice versa.

Solve for x.

x/6.8 = 5

~Multiply 6.8 to both sides

x/6.8 * 6.8 = 5 * 6.8

~Simplify

x = 34

Best of Luck!

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